Because the position of the vdW peak maximum ( D max) is often hidden within the dataset for other contacts (Figure 1b), the sum of vdW radii is normally taken as the half-height of the vdW peak distance, D half instead of the D max (Figure 1a).
6, 9, 10 Such distributions represent a superposition of a gaussian curve due to the vdW peak, and a rapidly growing function due to the randomly distributed contacts (Figure 1a). Conventionally, R vdW are derived from the position of the vdW peak in the distributions of contact distances between nonbonded atoms (Figure 1a,b). This inconsistency is rooted in the indirect nature of the approaches used to obtain the vdW parameters from experimental structural datasets. The question arises: why are all bonds in these crystals longer than the distance, which is usually considered as the most probable, in other words, closest to the energy minimum of the respective interatomic potential? 7 Moreover, about 2.0 % (>4000) of unique organic molecular crystals in the Cambridge Structural Database (CSD) 8 do not contain intermolecular contacts shorter than the sum of R vdW B° ndi (see the first section of Supporting Information for details). The latter can only be achieved at a very high pressure of ca. An illustrative example is a C 2Cl 6 crystal with the shortest r(Cl ⋅⋅⋅ Cl)=3.65 Å that exceeds significantly the 2 R vdW B° ndi (Cl)=3.50 Å. However, it has been noted 4, 5 that the sum of R vdW for available vdW sets including the most widely used one tabulated by Bondi 6 consistently underestimate the position of the energy minimum by as much as 0.3–0.4 Å. 3 These models operate – directly or indirectly – by the intermolecular interatomic distances, which are regarded as corresponding to the minimum energy of atom-atom interactions, and are usually defined as a function of the sum of vdW radii. Even though this concept has little physical grounding, it is easily interpretable and therefore widely used in the theoretical chemistry, particularly in design of force fields (in the Lennard-Jones parameter form), 1 dispersion corrections, 2 and COSMO-RS-type solvate models. The visual perception and basic analysis of chemical structures and architectures are strongly related to the concept of vdW radii, which provides the basic definition of the atomic “sizes”. Van der Waals (vdW) radii ( R vdW) are one of the cornerstones of contemporary chemistry.
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